A299630 Decimal expansion of 2*W(3/2), where W is the Lambert W function (or PowerLog); see Comments.

1, 4, 5, 1, 7, 2, 2, 7, 1, 5, 5, 3, 2, 4, 5, 2, 5, 1, 4, 0, 9, 7, 3, 7, 8, 7, 9, 8, 5, 5, 2, 6, 1, 3, 7, 5, 9, 4, 1, 2, 3, 2, 5, 6, 9, 9, 0, 0, 8, 5, 7, 3, 9, 6, 7, 0, 3, 1, 4, 8, 0, 5, 0, 8, 5, 7, 2, 5, 2, 5, 6, 9, 5, 2, 6, 5, 9, 5, 3, 4, 6, 2, 7, 1, 0, 0

Offset

0,2

Comments

The Lambert W function satisfies the functional equations

W(x) + W(y) = W(x*y(1/W(x) + 1/W(y)) = log(x*y)/(W(x)*W(y)) for x and y greater than -1/e, so that 2*W(3/2) = W(9/2)/(1/W(3/2)) = 2*log(3/2) - 2*log(W(3/2)). See A299613 for a guide to related sequences.

Links

Table of n, a(n) for n=0..85.

Eric Weisstein's World of Mathematics, Lambert W-Function

Example

2*W(3/2) = 1.451722715532452514097378798552...

Mathematica

w[x_] := ProductLog[x]; x = 3/2; y = 3/2; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]]  (* A299630 *)

Prog

(PARI) 2*lambertw(3/2) \\ Altug Alkan, Mar 13 2018

Crossrefs

Cf. A299613, A299631.

Sequence in context: A069284 A272638 A365464 * A068447 A237109 A199384

Adjacent sequences: A299627 A299628 A299629 * A299631 A299632 A299633

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 13 2018

Status

approved